In the eleventh and twelfth centuries in England, Wales and Normandy, Royal Acta were legal documents in which witnesses were listed in order of social status. Any bishops present were listed as a group. For our purposes, each witness-list is an ordered permutation of bishop names with a known date or date-range. Changes over time in the order bishops are listed may reflect changes in their authority. Historians would like to detect and quantify these changes. There is no reason to assume that the underlying social order which constrains bishop-order within lists is a complete order. We therefore model the evolving social order as an evolving partial ordered set or {\it poset}. We construct a Hidden Markov Model for these data. The hidden state is an evolving poset (the evolving social hierarchy) and the emitted data are random total orders (dated lists) respecting the poset present at the time the order was observed. This generalises existing models for rank-order data such as Mallows and Plackett-Luce. We account for noise via a random ``queue-jumping'' process. Our latent-variable prior for the random process of posets is marginally consistent. A parameter controls poset depth and actor-covariates inform the position of actors in the hierarchy. We fit the model, estimate posets and find evidence for changes in status over time. We interpret our results in terms of court politics. Simpler models, based on Bucket Orders and vertex-series-parallel orders, are rejected. We compare our results with a time-series extension of the Plackett-Luce model. Our software is publicly available.

翻译：在11至12世纪的英格兰、威尔士与诺曼底地区，皇家特许状是记录见证人按社会地位排序的法律文件。在场主教均以群体形式列于其中。就本研究而言，每份见证人名单可视为具有明确日期或时间范围的主教姓名有序排列。主教排序随时间的变迁可能反映其权威地位的变化。历史学者亟需探测并量化这些变化。制约名单内主教排序的潜在社会秩序并无理由被假定为全序关系。因此，我们将演进中的社会秩序建模为动态偏序集。针对此类数据构建隐马尔可夫模型：隐状态为演进中的偏序集（动态社会等级体系），观测数据为符合当时偏序结构的随机全序（带日期列表）。该模型推广了Mallows与Plackett-Luce等现有排序数据模型。通过随机"插队"过程处理噪声干扰。我们为偏序集随机过程设计的潜变量先验具有边缘一致性：参数控制偏序集深度，行动者协变量则影响其在等级体系中的位置。通过模型拟合与偏序集估计，发现了地位随时间演变的证据。结合宫廷政治背景对结果进行阐释。基于桶序与顶点级并联序的简化模型均被否定。与Plackett-Luce模型的时间序列扩展版本对比显示，本模型具有更优表现。相关软件已公开提供。